A team of UCLA scientists has been awarded a prestigious $1 million grant from the W.M. Keck Foundation for research aimed at reshaping and improving how images and large data sets are collected and analyzed in science, engineering, medicine and other fields.

Paul S. Weiss

"The Keck Foundation grants are very competitive, and we are honored to be selected," said Joseph Rudnick, dean of the UCLA Division of Physical Sciences and senior dean of UCLA's College of Letters and Science. "An outstanding team of UCLA scientists has put together three of UCLA's great strengths — imaging, mathematics and nanoscience — and their selection by the Keck Foundation is well-deserved."

The UCLA project will expand real-world applications of "compressive sensing," a method that uses mathematical algorithms to reconstruct complex medical and scientific images and data sets precisely from sparse amounts of information — similar to an artist accurately filling in the details of a face when given a simple outline of its features.

"Our goal is to leverage mathematical advances to transform the way imaging and related data are acquired, analyzed and understood," said the project's lead principal investigator, Paul S. Weiss, director of UCLA's California NanoSystems Institute (CNSI) and a distinguished professor of chemistry and biochemistry and of materials science and engineering who holds UCLA's Fred Kavli Chair in Nanosystems Sciences. "The result will be richer, more meaningful data through significant changes in how experiments are currently conducted and analyzed. In so doing, we hope to advance the science of imaging.

"If we are successful," he said, "the advances will apply broadly across many fields. We are uniquely placed to develop the theory, to carry out the initial experiments, to generalize the results and to disseminate the tools we create."

In addition to Weiss, principal investigators on the project are Andrea Bertozzi, director of computational and applied mathematics at UCLA and a professor of mathematics who holds UCLA's Betsy Wood Knapp Chair in Innovation and Creativity; Mark Cohen, director of the National Institutes of Health–funded UCLA Semel NeuroImaging Training Program and a UCLA professor of psychiatry with joint appointments in psychology, neurology, radiology, biomedical engineering and biomedical physics; and Stanley Osher, a UCLA professor of mathematics, computer science and electrical engineering and one of the most cited authors in mathematics and computer science.

"These UCLA scientists are world leaders in imaging and applied mathematics, uniquely capable of tackling these challenges," said Steven Beckwith, vice president for research and graduate studies at the University of California.

Compressive sensing, in its most basic sense, is a means of constructing more using less. Consider a sentence that contains only consonants and no vowels. When you look at "wrds wth nly cnsnnts nd n vwls," your brain fills in the missing vowels to form the complete, accurate sentence. Compressive sensing algorithms do the same thing with images when there is a similar sparsity of information. This means, for instance, that less visual data are required to construct clear and accurate images — whether for an MRI image of a kidney, a microscopic image of a virus or a simple photograph of a sunset.

The UCLA project, called "Leveraging Sparsity," will expand on the idea of using sparse data to make the collection and analysis of imaging and related data faster and more effective.

"The dramatic advances that have been made recently in pure and applied mathematics now allow us to collect a small number of samples while still creating detailed images from them," Cohen said. "We propose that the proven fact that, in general, images can be formed from just a few samples reflects a natural property of the world: it is 'sparse.' This research program, 'Leveraging Sparsity,' proposes to extend these concepts to very different data, including the control of nanoscale instrumentation, the prediction of neurological disease and to modern-day 'brain-reading.' These are only a few examples of the myriad ways that the concepts of sparse data collection can be applied to an endless variety of challenging and practical problems."

Explaining the concept, Osher said all of the photographic images and movies that we view and save are compressed, which means they take up much less digital space than the raw numbers of pixels that each one possesses. The information "can be contained in less space because, for example, some areas do not vary much or, in movies, do not vary significantly in time."

"That is the basis for JPEG and MPEG files," Osher added, referring to the formatting program that takes raw photos or videos and compresses them down to a fraction of their original size by removing a large percentage of their pixels — while retaining the images' essential details.

"So, one way to think about what we are doing," he said, "is to figure out where the information is the richest or, as we proceed, where it is needed the most to get a nearly complete picture — pardon the pun — and then to program our instruments to record it there."

New methods, he said, will have "extraordinary advantages."

Detecting epilepsy

One area of research the group will pursue is the detection of epilepsy, where conventional analysis is often inadequate, the scientists said.

"Compressive sensing methods are revolutionizing many areas of image processing, such as MRI," Bertozzi said. "The challenge is how to develop these techniques for complex multi-modal data (for example, MRI and EEG used jointly to diagnose epilepsy) and for data collected on extreme length scales, such as for nanoscale science," Bertozzi said. "Our project will leverage sparsity in these diverse data sets to develop new algorithms for a suite of important scientific problems."

"Medical data are expensive to acquire and frequently are difficult to interpret," said Cohen, whose research focuses on imaging and neuroscience. "With funding from the Keck Foundation, we will explore the very difficult problem of epilepsy, for which even the best diagnostic data are sometimes inconclusive. We believe that understanding the ways in which complete data sets — analogous to complete images — can be formed from sparse samples will help us to extract better and more accurate diagnoses from the limited data that can be acquired from people being evaluated for epilepsy."

Improving brain-imaging

Brain-imaging techniques, especially functional magnetic resonance imaging (fMRI), allow scientists to observe physical changes in the brain associated with human thinking and behavior. However, the information contained in the fMRI images can be difficult to interpret.

"Our team believes that there is an inherent sparsity to the operations of the brain that can be both exposed and exploited through the mathematics of compressive sensing," Cohen said. "By enabling us to break these complex imaging data into a small number of sparse features, the Keck funding will allow us to develop much more efficient and accurate means to translate the brain images of people to an understanding of the mental activities in which they are engaged.

"The advances developed through this work will also help patients. For example, harmful doses of ionizing radiation required by some diagnostic techniques, such as computed tomography (CT), can be reduced several-fold without a loss in clinical image quality," he said.

"What makes our team unique is the combination of novel and very successful algorithms in imaging, compressed sensing and optimization, together with the expertise in atom-scale imaging, fMRI, and brain decoding and our history of interdisciplinary research," Osher said.

"We believe this research will have important impact on science, engineering and medicine," Weiss said. "Our goal is to start a new field and to revolutionize how we record and analyze images and sequences of images. As it turns out, we also really enjoy working — and playing — together."

One of the missions of the California NanoSystems Institute (CNSI) at UCLA is to foster unique collaborations, and the four investigators strengthened their friendship as they met to discuss their ideas and to learn from one another.

"It has been great to put our heads, ideas, and fields together, and now it will be even better to get started," Weiss said. "Sparse data collection and reconstruction, thus far exploited principally for image data, represent recent and continuing discoveries in applied mathematics with the potential to be truly transformative across the many domains of data collection and information extraction."

The W.M. Keck Foundation was established in 1954 in Los Angeles by William Myron Keck, founder of the Superior Oil Company. Supporting pioneering discoveries in science, engineering and medical research has been the foundation's mandate for more than half a century.